Question

The number of database queries made during any interval of time is a Poisson random variable....

The number of database queries made during any interval of time is a Poisson random variable. On average, six queries are made every minute. Determine the probability that three or more queries will be made during an interval of 15 seconds.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that ,

mean = = 6

Using poisson probability formula,

P(X = x) = (e- * x ) / x!

P(X 3) = 1 - P(X 2 )

= 1 - (  P(X = 0) + P(X = 1) + P(X = 2))

= 1 - (  (e6 * 60) / 0! + (e6 * 61) / 1! + (e6 * 62) / 2!

= 1 - (0.0025+0.0149+0.0446)

= 1 - 0.0620

= 0.9380

The probability that three or more queries will be made during an interval of 15 seconds is 0.9380.

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